Meteorites and the Chemical Evolution of the Milky Way

Transcription

1 Meteorites and the Chemical Evolution of the Milky Way Larry R. Nittler Department of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 Broad Branch Road NW, Washington, D. C , USA and Nicolas Dauphas Origins Laboratory, Department of the Geophysical Sciences, Enrico Fermi Institute, and Chicago Center for Cosmochemistry, The University of Chicago, 5734 South Ellis Avenue, Chicago, IL 60637, USA. (Meteorites and The Early Solar System 2; Final version April 6, 2005) The theory of Galactic Chemical Evolution (GCE) describes how the chemical and isotopic composition of galaxies changes with time as succeeding generations of stars live out their lives and enrich the interstellar medium with the products of nucleosynthesis. We review the basic astronomical observations that bear on GCE and the basic concepts of GCE theory. In addition to providing a standard set of abundances with which to compare GCE predictions, meteorites also provide information about how the Galaxy has evolved through the study of preserved presolar grains and radioactive isotopes. 1. Introduction The Solar System is situated in the disk of the Milky Way galaxy, some 8.5 kiloparsecs from the Galactic center. It formed Gyr ago (Amelin et al., 2002) and its composition represents a snapshot of the composition of the Milky Way in the solar neighborhood at that time. The bulk composition of the Solar System has often been referred to as the cosmic composition (Anders and Grevesse, 1989), with the underlying assumption that it represents the average composition of the Galaxy. However, stellar nucleosynthesis is a phenomenon that is discrete in both time and space. The concept of cosmic composition therefore breaks down when the chemical and isotopic composition of the Galaxy is examined at a fine scale and astronomy abounds with examples of

2 2 objects and environments with non-solar compositions. Galactic Chemical Evolution (GCE) is the name given to the theory of how the chemical composition of a galaxy varies with time and space as succeeding generations of stars live out their lives and enrich the interstellar medium (ISM) with the products of nucleosynthesis. Note that the word chemical is somewhat misleading in this context, since GCE refers only to the abundances of nuclei in the Galaxy, not to the chemical state in which they might appear. In this chapter, we discuss some of the ways in which meteorites can help unravel the presolar nucleosynthetic history of the Milky Way. A key constraint for models of GCE has long been the solar isotopic and elemental abundance pattern, largely determined by measurements of CI chondrites. However, meteorites also preserve a record of GCE in the form of preserved presolar dust grains and extinct radioactivities. Here, we will review the basic concepts of GCE theory and astronomical constraints before considering the role of GCE in determining the isotopic compositions of presolar grains and the abundances of radioactivities in the early Solar System. Although the subject of GCE has a rich history, we concentrate on recent developments of the field. The reader is referred to the excellent books by Pagel (1997) and Matteucci (2003) for comprehensive reviews of the rich astronomical literature on the topic. 2. Basic concepts and astronomical constraints Excluding dark matter, the Milky Way consists of several components, including a thin disk (to which the Solar System belongs), a thick disk, a bright inner bulge, and a large spherical diffuse stellar halo. Just how these components formed is not known, but there are several competing models (Matteucci, 2003). Most likely, both primordial collapse of a protogalactic gas cloud and subsequent accretion and merger of smaller systems have played a role (Gibson et al., 2003). However, many aspects of GCE modeling do not depend strongly on the overall model of galactic formation. Because the Solar System belongs to the thin disk, we will primarily concentrate on observations and GCE models of this component. A crucial quantity involved in any discussion of GCE is metallicity, which is the abundance of elements heavier than He ( metals for astronomers). The letter Z is usually used to indicate the total metallicity. However, the normalized iron abundance ([Fe/H] = log (Fe/H) log (Fe/H) ) is often used as a proxy for total metallicity, as Fe is relatively easy to measure in a large number of astronomical environments. The metallicity of the Sun (Z ) has long been thought to be 2%, but a recent downward revision in the solar oxygen abundance by Allende Prieto et al. (2001) now indicates that it is closer to 1.4%. Descriptions and models of GCE require a number of key ingredients:

3 3 Boundary conditions: The initial composition (often taken to be that generated by the Big Bang) and whether the system is closed or open must be defined. Stellar yields: The abundances of isotopes produced by nucleosynthesis in stars of various types are required. These are determined by stellar evolutionary calculations coupled to nuclear reaction networks (e. g., Meyer and Zinner, 2005). In general, the nucleosynthesis abundance patterns ejected by stars depend critically on the stellar mass and metallicity. Moreover, there are still large uncertainties in the predicted yields due to uncertainties in the stellar evolution physics and nuclear reaction cross sections. A key concept related to stellar yields is the definition of primary and secondary species. A primary specie is one that can be synthesized in a zero-metallicity star, consisting initially of pure H and He. Examples of primary species are 16 O and 12 C, both made by stellar He burning. In contrast, nucleosynthesis of a secondary specie requires some pre-existing metals to be present in the star. Some secondary species include the heavy isotopes of O, mbox 14 N and the s-process elements (Meyer and Zinner, 2005). The star formation rate (SFR) is usually parameterized in GCE models. A very common parameterization is to assume that the SFR is proportional to the disk gas surface density (σ g ) to some power: Ψ σ n, where n=1 2 (Schmidt, 1959). However, there are many examples of more complicated expressions for the SFR (e. g., Dopita and Ryder, 1994, Wyse and Silk, 1989). The initial mass function (φ(m)) describes the number distribution of stars which form in a given mass interval at a given time. It is usually parameterized as a single- or multicomponent power law, for example the common Salpeter (1955) IMF is: φ(m) M Other parameterizations have different power-law indices for different mass ranges (Scalo, 1986). In most models it is assumed that the IMF is constant in space and time; this is consistent with observational evidence (Kroupa, 2002). Except for the simplest models (see next section), infall of gas from the halo onto the disk and outflows from galactic winds are often included in GCE models. The infall rate is usually assumed to vary with galactocentric radius and decrease with time. There is evidence for at least two independent episodes of infall leading to the formation of the halo and the thin disk, respectively (Chiappini et al., 1997). GCE models are constrained by a number of disparate observational data. These include the present-day values of the star formation and supernova rates, the present-day values of the surface mass density of stars and gas (Fig. 1), stellar mass function and gas infall rate, as well as chemical abundances measured in a wide variety of stars and interstellar gas. The abundance data can be divided into a number of constraints:

4 4 The Solar abundances: The composition of the Sun (e. g., Anders and Grevesse, 1989), determined both by spectroscopy of the Sun and analysis of CI chondrites, represents a sample of the ISM 4.6 Gyr ago and GCE models of the Milky Way disk should reproduce it (Timmes, Woosley and Weaver, 1995). For many elements and isotopes, the Solar System abundances are the only extant data with which to compare GCE models. The age-metallicity relationship (AMR): The measured metallicity of stars decreases on average with stellar age (Twarog, 1980, Edvardsson et al., 1993), as would be expected from the basic idea of GCE. However, there is a large observed scatter in metallicity, greater than a factor of two, for stars of a given age in the solar neighborhood (Edvardsson et al., 1993;Rocha-Pinto et al., 2000) This scatter is still not well-explained and makes the AMR a rather weak constraint for GCE models. Abundance ratio evolution: Because different elements are formed by different nucleosynthetic processes, they can evolve at different rates. Thus, studies of element abundance ratios as a function of metallicity can provide important information about GCE (McWilliam, 1997). For example, low-metallicity stars have higher-than-solar ratios of so-called α elements (e.g., 16 O, 24 Mg) to iron, but these ratios decrease to solar as solar [Fe/H] is reached. This reflects the fact that the α elements are made primarily in Type II supernovae, which evolve rapidly ( 10 7 yr), whereas a major fraction of Fe in the Galaxy is made by Type Ia supernovae, which evolve on much longer timescales ( 10 9 yr). Thus, high α/fe ratios at low metallicities indicate that Type Ia supernovae had not yet had time to evolve and enrich the ISM with their ejecta. The exact shape of abundance trends are determined by the relative fractions and timescales of Type Ia and II supernovae as well as other details of GCE. The G-dwarf metallicity distribution: G-dwarfs are low-mass stars ( M ) that have lifetimes greater than or equal to the age of the disk. These stars are not active sites of nucleosynthesis and the compositions of their envelopes reflect the compositions of the interstellar gas from which they formed. Thus, their metallicity distribution (Fig. 2) represents a history of the star formation rate since the Milky Way formed (van den Bergh, 1962; Schmidt, 1963; Jørgensen, 2000). As discussed below, the simplest closed-box GCE models overpredict the number of low-metallicity G dwarfs. G-dwarfs are actually massive enough that some of them have begun to evolve away from the main sequence, which requires that a correction be applied to the metallicity distribution. Note however that stars with lower masses such as K or M-dwarfs show the same discrepancy between the observed and the predicted abundance of metal deficient stars (Kotoneva et al., 2002). Various approaches have been adopted for solving this problem, including preenrichment of the gas, varying initial mass function, or gas infall. Among these, infall of low-metallicity gas on the galactic plane is the most likely culprit. At present, so-called high velocity clouds are seen falling on the galactic disk. Some

5 5 of these clouds have the required low metallicity (down to 0.1Z ) to solve the G-dwarf problem (Wakker et al., 1999). Abundance gradients: Observations of abundances in molecular clouds, stars and planetary nebulae at a range of distances from the galactic center indicate the presence of metallicity gradients, where the inner Galaxy is more metal-rich than the outer galaxy (Matteucci, 2003). This result indicates that the Milky Way disk formed in an inside-out fashion, with the inner disk forming on a shorter timescale than the outer disk. The precise values for metallicity gradients expected for the disk depend strongly on the balance between the radial dependences of the SFR and the infall rate. 3. GCE models With the ingredients and observational constraints described in the previous section, models of GCE can be constructed. We first consider homogeneous models. These (semi-)analytic models make simplifying assumptions that allow the calculation of the mean properties and elemental abundance evolutionary trends of galactic systems. Most homogeneous GCE models of the galactic disk assume cylindrical symmetry and neglect both the finite thickness of the disk and any possible radial flows of matter. Thus, the only relevant spatial variable is the galactocentric radius and what is calculated is the mean abundance evolution within annuli about the Galactic center. We first consider an oversimplified, but illustrative, case: the so-called Simple model (e. g., Schmidt, 1963; Pagel, 1997; Matteucci, 2003) (Fig. 1). Let us denote Z i the mass fraction of nuclide i in the ISM. The Galaxy formed from gas of low metallicity (Z i0 = 0). No mass loss or gain occurs during the galactic history (closed-box model). If E(t) is the rate of gas ejection (per unit surface area of the disk, Fig. 1) from late evolving stars and Ψ(t) is the rate of gas accretion on nascent stars, then the rate of change of the gas surface density can be written as: The rate of change of the abundance of any nuclide i is: dσ g /dt = E Ψ. (1) d(z i σ g )/dt = Z i,e E Z i Ψ Z i σ g /τ, (2) where Z i,e is the mass fraction of i in the ejecta of all stars and τ is the mean-life (if the nuclide is radioactive). There is no delay between accretion of gas in stars and return of the nucleosynthetically enriched gas to the ISM (instantaneous recycling approximation). This assumption allows us to write E(t) = RΨ(t), where R is the so-called return fraction, the rate at which mass is returned to the ISM. That is, as soon as a generation of stars is formed, a fraction R instantaneously comes

6 6 back out, and a fraction (1 R) remains locked up in stars (white dwarfs, etc) which do not return mass to the ISM. After some rearrangement and combining equations (1) and (2), it is straightforward to show that: dz i /dt = RΨ(Z i,e Z i )/σ g Z i /τ. (3) Defining the yield y as the quantity of newly synthesized matter per unit mass of stellar remnants: y = R(Z i,e Z i )/(1 R), (4) and assuming a metallicity-independent yield (Z i,e Z i is constant) and a linear star formation rate: Ψ = ωσ g /(1 R), (5) it follows that This equation can be integrated by the method of varying constant, dz i /dt = yω Z i /τ. (6) Z i = yωτ ( 1 e t/τ ). (7) In the limit of a stable nuclide (τ ), the previous equation assumes the form: Z i (τ ) = yωt. (8) An immediately obvious result is that the Simple model predicts that the abundance of a stable primary isotope (whose yield y is independent of time and metallicity) increases linearly with time. Moreover, and of great importance to the interpretation of presolar grain data ( 6), the Simple model also predicts that the ratio of a secondary isotope to a primary one increases linearly with total metallicity (Pagel, 1997). Note that a great deal of physics is hidden by the formulation above. For example, actual calculation of y requires integrating nucleosynthetic yields of stars of different mass over the initial mass function. We will revisit the linear closed-box model and its predictions for radioactive nuclei in 4. The main virtue of this model is its simplicity. However, the Simple model fails to explain the G-dwarf metallicity distribution (Fig. 2) in that it predicts far more metal deficient stars than what is observed. This is known as the G-dwarf problem. As discussed in the previous section, it now appears most likely that the discrepancy is due to the closed-box assumption; gas flows, especially infall of low-metallicity gas on the disk, must be included in GCE models. Beyond the G-dwarf problem, the Simple model also breaks down when trying to describe the evolution of elements produced by long-lived stars, for which the instantaneous recycling approximation is not

7 7 valid. Moreover, the observed age-metallicity relationship for stars in the solar neighborhood is not well described by Eq. 8. Thus, more realistic models of GCE are needed. Including infall in an analytic GCE model requires parameterization of the infall rate (e. g., Larson, 1974; Lynden-Bell, 1975). Clayton (1985) provided a very flexible family of GCE models, which he called a Standard model. These models are exactly soluble and allow great freedom in parameterizing both the star formation rate and the infall rate. Clayton s Standard model is very useful for understanding the physical behavior of Galactic gas without resorting to numerical calculations. Pagel (1989) modified Clayton s model to include a fixed time delay for elements produced by long-lived stars (e.g., Fe, s-process elements). Although sophisticated analytical GCE formalisms, like those of Clayton (1985) and Pagel (1989), are very useful for providing gross physical understanding of GCE, more realistic models require complete relaxation of the instantaneous recycling approximation and closed-box assumptions. Such models do not usually have analytical solutions and require numerical calculation. Typical formalisms (e. g., Matteucci and Greggio, 1986; Timmes et al., 1995) require solving coupled integro-differential equations with separate terms describing ISM enrichment by stellar ejecta, star formation, infall, outflow and radioactive decay, respectively: d dt σ i(r, t) = MU M L ψ(r, t τ m )X mi (t τ m )φ(m)dm Z i (r, t)ψ(r, t) (9) + d dt σ i(r, t) infall d dt σ i(r, t) outflow σ i (r, t)/τ i, where σ i (r, t) is the surface mass density of gas in the form of isotope i at galactocentric radius r and time t, M L and M U are the lower and upper mass limits, respectively, of stars which enrich the ISM at a given time, ψ is the star formation rate, X mi is the mass fraction of i ejected by a star of mass m, φ is the initial mass function, τ m is the lifetime of a star of mass m, Z i (t) is the mass fraction of i in the ISM at time t, and τ i is the mean lifetime for isotope i. In fact, the first term is often divided into separate integrals for the ejecta from single stars and binary stars, since a fraction of the latter will result in supernovae of Type Ia and/or novae (Matteucci and Greggio, 1986; Roman and Matteucci, 2003). A large number of numerical homogeneous GCE calculations including infall and neglecting the instantaneous recycling approximation have been reported in recent years. Some general conclusions can be drawn from many of these models: 1) The solar abundances of most isotopes up to Zn can be reproduced to within a factor of two (Timmes et al., 1995), in most cases discrepancies are due to uncertainties in the nucleosynthetic processes and yields responsible for the specific isotope. (2) The G-dwarf metallicity distribution can be quite well approximated if the local disk

8 8 formed by infall of extragalactic gas over a period of several Gyr. (3) The observed abundance ratio trends (e.g., O/Fe versus Fe/H) are well explained by the time delay between supernovae of Type Ia and Type II. (4) To explain abundance gradients, the disk must have formed inside-out with a strong dependence of the star formation rate on galactocentric radius. Despite the success of modern GCE models in reproducing a large number of observational constraints, it should be remembered that there are still many crucial uncertainties. Of particular concern are remaining uncertainties in the nucleosynthetic yields of many isotopes, especially those of the iron-peak elements, as well as the precise form and possible spatial or temporal variability of the initial mass function. The homogeneous models described above explain well many of the average properties of the Galaxy, for example the average element/fe ratios measured in stars of a given metallicity. However, because of the discrete and stochastic nature of star formation and evolution, local chemical heterogeneities about mean trends are to be expected. Observationally, the scatter in elemental abundances in stars increases with decreasing metallicity. This is especially true for the lowmetallicity stars of the galactic halo. Although there is a very large scatter in metallicity for disk stars of a given age in the solar neighborhood (Edvardsson et al., 1993; Reddy et al., 2003), metal abundance ratios (e.g., Mg/Fe) in the disk do not show resolvable scatter around the mean trends with metallicity. A number of heterogeneous GCE models have been published which attempt to explain abundance scatter (and its decrease with increasing metallicity) in the halo (Argast et al., 2000; Oey, 2000; Travaglio et al., 2001) and the large scatter of metallicity in the disk (e. g., Copi, 1997; Van den Hoek and De Jong, 1997). We will consider the issue of heterogeneous GCE and its effects on presolar grain isotopic compositions in 6.1. In recent years, an additional class of GCE models has been explored, chemodynamical (GCD) models, in which the chemical evolution of the Galaxy is explicitly tied to its dynamical evolution. GCD models range from relatively simple models exploring the effects of radial diffusion of stellar orbits coupled to abundance gradients (Grenon, 1987; François and Matteucci, 1993; Clayton, 1997) to quite sophisticated three-dimensional chemodynamic codes which attempt to self-consistently treat the dynamics of galactic gas, dust and dark matter along with abundance evolution (Raiteri et al., 1996; Brook et al., 2003). 4. Nuclear cosmochronology and extinct radioactivities Nuclear cosmochronology, also sometimes termed nucleocosmochronology, is the study of radioactive nuclei with the goal of constraining the timescales of nucleosynthesis and galaxy formation. This field takes its root in a paper published in 1929 where Rutherford first used uranium to estimate the age of the Earth and erroneously concluded that the processes of production of

9 9 elements like uranium were certainly taking place in the sun years ago and probably still continue today. Actually, the uranium in the Solar System was produced, together with other actinides, by the r-process of nucleosynthesis in very energetic events, before the birth of the solar system (Meyer and Zinner, 2005). The primary aspiration of nuclear cosmochronology historically has been to retrieve the age of the Milky Way and the duration of nucleosynthesis from the abundances of unstable nuclei measured in meteorites. The abundances of radioactive nuclides in the interstellar medium (ISM) represent a balance between production in stars and decay in the ISM (Tinsley, 1977, 1980; Yokoi et al., 1983; Clayton, 1985, 1988a; Pagel, 1997). These abundances depend very tightly on the dynamical evolution of the Galaxy. For instance, the abundances of radioactivities in the ISM would be different if all nuclides had been synthesized in a stellar burst shortly after the formation of the Galaxy or if they had been synthesized throughout the galactic history. Radioactivities therefore provide invaluable tools for probing the nucleosynthetic history of matter. In order to investigate the formation of the Solar System, one can either proceed forward or backward in time. The abundances of radioactive nuclides in the ISM at solar system birth can be theoretically predicted from models of GCE and stellar nucleosynthesis. The abundances of radioactive nuclides can also be determined from laboratory measurements of extraterrestrial materials, for example by detection of decay products of now-extinct nuclides. Comparisons between the predicted and the observed abundances provide unequaled pieces of information on galactic nucleosynthesis history and the origin of short-lived nuclides in the early solar system Modeling the remainder ratio When investigating radionuclides in the ISM, it is useful to introduce the remainder ratio (R), which is the ratio of the abundance of an unstable nuclide to its abundance if it had been stable (Clayton, 1988a; Dauphas et al., 2003), R = N(τ)/N(τ ). (10) If R is the ratio of the unstable nuclide to another stable nuclide cosynthesized at the same site and P is the production ratio, then the remainder ratio in the early solar system (ESS) can be calculated as follows, R ess = R/P. (11) The remainder ratio in the ISM at the time of solar system formation can be calculated in the framework of GCE models. Let us begin with the Simple GCE model discussed in Section 3. (Fig. 1). The remainder ratio in the ISM (Eq. 10) can be calculated from Eq. 7: R ism = τ T (1 e T/τ ), (12)

10 10 the presolar age of the Galaxy is denoted T (T = T G T, where T G is the age of the Galaxy and T is the age of the solar system). Thus, in the closed-box linear model, the remainder ratio of a given nuclide depends on its mean-life τ and on the presolar age of the galactic disk T. For short-lived nuclides (τ << T), the remainder ratio becomes: R ism = τ/t. (13) For very short-lived species, the timescale of ISM mixing is longer than the mean-life of the nuclide, granularity of nucleosynthesis must be taken into account, and the notion of steady-state abundances is inappropriate. Meyer and Clayton (2000) estimated that the cut where the concept of steady-state abundances breaks down must be for mean-lives around 5 My. As discussed earlier, the Simple model fails to explain important astronomical observations, notably the G-dwarf metallicity distribution. Clayton (1985, 1988a) estimated the remainder ratio for short-lived nuclides in the context of a parameterized linear infall model. More recently, Dauphas et al. (2003) improved over this model using a more realistic non-linear parameterization of the star formation rate (dσ g /dt = ωσg n, with n close to 1.4, Gerritsen and Icke, 1997; Kennicutt, 1998; Kravtsov, 2003) and a parameterized infall rate following Chang et al. (1999). As discussed by Clayton (1988a) and Dauphas et al. (2003), when infall of low-metallicity gas is taken into account, Eq. (13) for the remainder ratio for short-lived nuclides is not valid and the following expression should be used instead: R ISM = κτ/t. (14) The numerical GCE model of Dauphas et al. (2003) gives κ = 2.7 ± 0.4 (unless otherwise indicated, all errors in this Chapter are 2σ), which is identical within uncertainties to the range of values advocated by Clayton (1985) of 2 < κ < 4. For long-lived radionuclides, Clayton (1988a) derived an analytic solution for the remainder ratio. If nonlinearity is taken into account, the remainder ratio must be calculated numerically (Eq. 4 of Dauphas et al., 2003) The age of the Galaxy and the U/Th production ratio As illustrated in the previous section, the remainder ratio in the ISM at the time of solar system formation depends on the age of the galactic disk. For short-lived radionuclides, it is possible that significant decay can occur between the last nucleosynthesis event and actual incorporation into the Solar System s parent molecular cloud core (see 4.3). For long-lived radionuclides, however, such a free-decay interval can be neglected and the remainder ratio in the ISM must be equal to that in the ESS. It is thus possible to determine the age of the Galaxy if a GCE model is specified, if the abundance of the considered radionuclide in the ESS is known, and if its production ratio normalized to a neighbor nuclide cosynthesized at the same site is known. The first meaningful

11 11 attempt to calculate the radiometric age of the Milky Way was reported in the seminal paper of Burbidge et al. (1957). Using a U/Th production ratio of 0.64 and a model of constant production, they estimated an age of approximately 10 Gyr for the Galaxy. In the last 50 years, multiple studies have addressed this question and the reader will find ample details in some of these contributions (Tinsley, 1980; Yokoi et al., 1983; Clayton, 1988a; Cowan et al., 1991; Meyer and Truran, 2000). Clayton (1988a) evaluated potential nuclear cosmochronometers and concluded that the pair 238 U (τ = yr) Th (τ = yr) gives the most stringent constraint on the age of the galactic disk. We shall therefore focus our discussion on the 238 U/ 232 Th ratio, which will simply be denoted U/Th hereafter. There are two approaches that can be used to estimate the age of the Milky Way based on the U/Th ratio. One relies on the determination of this ratio in the spectra of low-metallicity stars in the halo of the Galaxy. The second relies on the U/Th ratio measured in meteorites and makes use of galactic chemical evolution models. The U/Th ratio measured in meteorites (Chen et al., 1993; Goreva and Burnett, 2001) is the result of an interplay between production in stars, enrichment of the gas by stellar ejecta, and decay in the ISM. Because U decays faster than Th, its ratio in the ISM changes with time. If one specifies the history of nucleosynthesis before solar system formation, a relationship can be found between the U/Th production ratio, the ratio measured in the ISM at solar system formation (as recorded in meteorites), and the age of the Galaxy. For instance, let us consider that actinides were all synthesized at the time the Galaxy formed and that they were not subsequently replenished (initial stellar burst scenario). In this case, we can write a simple free-decay equation where R U/T h R U/T h = P U/T h e (λ T h λ U )(T G T ), (15) is the ratio in the ISM at solar system formation, P U/T h is the production ratio, and T G is the total age of the Galaxy (to present). The ratio in the ISM (R U/T h ) is measured in meteorites; the production ratio (P U/T h ) can be derived from the theory of r-process nucleosynthesis. The age (T G ) can therefore be calculated. Of course, all actinides were not produced in an initial burst and it is thus necessary to consider more realistic GCE models. Such models, describing enrichment of the ISM in actinides through time, can be constrained by a host of astronomical observations (Yokoi et al., 1983; Clayton, 1988a; Dauphas, 2005a), but a detailed discussion of how the models are parameterized and constrained is beyond the scope of this chapter. The most important feature of the models is that they incorporate infall of low-metallicity gas on the galactic plane. In a recent paper, Dauphas (2005a) showed that the relationship between the production ratio, the meteorite ratio, and the age of the Galaxy can be approximated by a simple formula, valid between 10 and 20 Gyr, P U/T h = R U/T h /(at G + b), (16) where a = and b = (see Dauphas, 2005a for details). The U/Th ratio in the ISM at solar system formation is ± (Chen et al., 1993). Goriely and Arnould (2001)

12 12 and Schatz et al. (2002) recently quantified the influence of nuclear model uncertainties on the r-process nucleosynthesis of actinides. The 238 U/ 232 Th production ratio is estimated by Schatz et al. (2002) to be 0.60 ± 0.14 while Goriely and Arnould (2001) propose a more conservative range of (error bars represent 68% confidence intervals). The range of production ratios estimated by modern r-process calculations encompasses the initial solar composition and the approach based on GCE can therefore only provide an upper limit on the age of the Galaxy. If we adopt P U/T h < 0.7, we can derive an upper limit for the age of the Milky Way of approximately 20 Gyr, which is useless in comparison to the precision with which the age of the Universe is known (13.7 Gyr, Spergel et al., 2003). This shows that the solar U/Th ratio alone cannot be used to constrain the duration of nucleosynthesis. The U/Th ratio measured in low-metallicity halo stars can also be used as a potential chronometer to determine the age of the Milky Way (Cayrel et al., 2001; Hill et al., 2002; Cowan et al., 2002). These stars formed very early in the galactic history and they inherited at their formation a U/Th ratio that must have been equal to the production ratio by r-process nucleosynthesis. Hill et al. (2002) measured the most precise U/Th ratio in the low-metallicity halo star CS of ± For such stars, a simple free decay equation can be written, P U/T h = R U/T h LMHS e(λ U λ T h )T G. (17) Again, the ratio R U/T h U/T h LMHS in low-metallicity halo stars can be measured, the production ratio P can be derived from the theory of r-process nucleosynthesis, and it is therefore possible to calculate the age of the Galaxy T G. Goriely and Arnould (2002) propagated the uncertainty on the production ratio and concluded that the age cannot be constrained to better than 9-18 Gyr. As in the case of GCE and the solar U/Th ratio, this range is of limited use when trying to establish the chronology of structure of formation in the Universe and other methods give more precise estimate of the age of the Galaxy (Krauss and Chaboyer, 2003; Hansen et al., 2004). The main source of uncertainty in calculations of the age of the Milky Way based on lowmetallicity halo stars and galactic chemical evolution is the U/Th production ratio. In a recent contribution, Dauphas (2005a) argued that because there are two equations (16 and 17) in two unknowns (P U/T h and T G ), the system could actually be solved (Fig. 3). The values that he derived for the age and the production ratio are Gyr and , respectively. The virtue of this approach is that a probabilistic meaning can be ascribed to the uncertainty interval and the U/Th production ratio can be determined independently of r-process calculations. The oldest stars in our Galaxy formed shortly after the birth of the universe (13.7 ± 0.2 Gyr, Spergel et al., 2003).

13 Short-lived nuclides in the early solar system The GCE models presented previously all assume that nucleosynthesis is a smooth function of time. Stars are actually discrete in both time and space. Long-lived radionuclides retain a long memory and deterministic models can be applied (Clayton, 1988a; Dauphas et al., 2003). In contrast, short-lived radionuclides may be affected by the nucleosynthetic history of the solar neighborhood right before solar system formation. For these nuclides, a stochastic treatment should be applied (e. g., Meyer and Luo, 1997). Very short-lived extinct radionuclides, such as 26 Al, might have been injected from a nearby giant star (asymptotic giant branch, AGB or supernova, SN) that might have triggered the protosolar nebula into collapse. In the present contribution, the discussion is limited to extinct radionuclides which have mean lives long enough that the composition of the ISM can be estimated in a deterministic way (τ > 5 My, Meyer and Clayton, 2000). This comprises the nuclides 53 Mn (mean-life 5.4 My), 92 Nb (50.1 My), 107 Pd (9.4 My), 129 I (22.6 My), 146 Sm (148.6 My), 182 Hf (13.0 My), and 244 Pu (115.4 My). The abundances of all these nuclides in the ESS are well known. For calculating the remainder ratio, the abundances of these nuclides must be normalized to the abundances of neighbor nuclides produced in the same stellar environment. Hence, the normalizing nuclides used in the present contribution are not always identical to those used in the initial publications reporting extinct nuclide abundances. For evaluating the remainder ratio in the ESS, the basic ingredients are the normalized abundances of the short-lived nuclides in the ESS at the time of calcium-aluminum-rich inclusion (CAI) formation and the associated production ratios. Manganese-53 is synthesized together with 55 Mn in massive stars. As discussed by Meyer and Clayton (2000), because solar system 53 Cr must have been primarily synthesized as 53 Mn, the production ratio 53 Mn/ 55 Mn can be approximated by the solar system 53 Cr/ 55 Mn ratio of 0.13 (Anders and Grevesse, 1989). The SN II models of Rauscher et al. (2002) predict a comparable production ratio, 53 Mn/ 55 Mn = 0.15, when individual yields from SN II of different masses are weighted by a typical initial mass function. Note that SNe II underproduce iron-peak nuclides relative to 16 O by a factor of 2-3 (Rauscher et al., 2002), the rest must be produced in SN Ia. This underproduction feature is reflected in the abundance patterns of low-metallicity halo stars (Wheeler et al., 1989; McWilliam, 1997). The initial 53 Mn/ 55 Mn ratio in CAIs is estimated to be 2.81 ± (Birck and Allègre, 1985; Nyquist et al., 2001). However, a lower initial value may be required in order to bring the chronologies based on the various extinct and extant radionuclides into agreement (Lugmair and Shukolyukov, 1998; Dauphas et al., 2005). We shall adopt here an initial ratio of 1.0 ± The remainder ratio is therefore R 53 ess = 7.7 ± Niobium-92 was most likely synthesized by the p-process in SN. This radionuclide cannot be normalized to another isotope of the same element because the only stable isotope of niobium,

14 14 93 Nb, was synthesized by the s-process. It can instead be normalized to 92 Mo, which is also a pure p-process nuclide. The 92 Nb/ 92 Mo production ratio during photodisintegration of seed nuclei in SNII is 1.5 ± (Rauscher et al., 2002; Dauphas et al., 2003). The initial ratio in meteorites is 2.8 ± (Harper, 1996; Schönbächler et al., 2002). The remainder ratio is therefore R 92 ess = 1.9 ± (Dauphas et al., 2003). Note that Münker et al. (2000) and Yin et al. (2000) found higher initial ratios but the CAI measurements of Münker et al. (2000) might have been affected by nucleosynthetic effects and the zircon measurement of Yin et al. (2000) was not replicated by Hirata (2001). The initial 107 Pd/ 110 Pd in the ESS was 5.6 ± (Kelley and Wasserburg, 1978; Chen and Wasserburg, 1996). This corresponds to 107 Pd/ 110 Pd r = 5.8 ± , where 110 Pd r is the r-process contribution to the solar abundance of 110 Pd (Arlandini et al., 1999). Palladium-107 is primarily a r-process nuclide that could also have received contribution from the s-process. For most r-process radionuclides, their production ratios can be reliably estimated by decomposing the abundances of their daughter nuclides into s and r-process contributions. For instance, the entire r-process abundance of 107 Ag must have been channeled through 107 Pd. The sites of r- nucleosynthesis are not well established but they very likely correspond to the late stages of rapidly evolving stars. The 107 Pd/ 110 Pd production ratio can therefore be approximated to the solar system 107 Ag r / 110 Pd r, where 107 Ag r and 110 Pd r are obtained by subtracting the s-process contribution to solar abundances (Arlandini et al., 1999). The 107 Pd/ 110 Pd r-process production ratio is therefore 1.36 and the remainder ratio is R 107 ess = 4.3 ± Iodine-129 is also primarily an r-process nuclide. It was historically the first short-lived nuclide to have been found to have been alive in the ESS (Reynolds, 1960). When the Pb/Pb age of Efremovka CAIs ( ± 0.6 Ma, Amelin et al., 2002) is combined with the observed 129 I/ 127 I- Pb/Pb age correlation in ordinary chondrite phosphates (Brazzle et al., 1999), the early solar system 129 I/ 127 I is estimated to be 1.19 ± This corresponds to a 129 I/ 127 I r initial ratio of 1.25 ± As discussed in the case of 107 Pd, the 129 I/ 127 I r-process production ratio can be estimated from decomposition of 129 Xe into r and s-processes (Arlandini et al., 1999). Because 129 Xe is predominantly synthesized by the r-process, little uncertainty affects the production ratio, 129 I/ 127 I = The remainder ratio for 129 I is R 129 ess = 8.6 ± Samarium-146 is a pure p-process isotope. The ESS 146 Sm/ 144 Sm ratio is 7.6 ± (Lugmair et al., 1983; Prinzhofer et al., 1992). It production ratio as obtained in the most recent models of the p or γ-process in SNe II is 1.8 ± (Rauscher et al., 2002; Dauphas et al., 2003). The remainder ratio is therefore R 146 ess = 4.2 ± (Dauphas et al., 2003). Hafnium-182 is presumably an r-process isotope. From the decomposition of the abundance of its daughter isotope 182 W into r and s-processes (Arlandini et al., 1999), the 182 Hf/ 177 Hf production ratio is estimated to be The initial 182 Hf/ 177 Hf ratio in the ESS is 1.89 ±

15 15 (Yin et al., 2002). Note that Quitté and Birck (2004) have derived a higher initial ratio from W isotope measurement of the Tlacotepec iron meteorite, but this may be affected by cosmogenic effects. The initial ratio of Yin et al. (2002) corresponds to 182 Hf/ 177 Hf r = 2.31 ± The remainder ratio is therefore R 182 = 2.86 ± Plutonium-244 is an r-process isotope. As with other actinides, its production ratio is uncertain because the closest stable r-process nuclide that can anchor the models is 209 Bi, 35 amu away. Goriely and Arnould (2001) evaluated nuclear model uncertainties on the production of actinides. Among the various models, only those that give a 238 U/ 232 Th production ratio consistent with meteoritic abundances are retained. The 244 Pu/ 238 U production ratio is thus estimated to be 0.53 ± The initial 244 Pu/ 238 U in the solar system is estimated to be ± (Rowe and Kuroda, 1965; Hudson et al., 1989). The ratio of the remainder ratios R 244 ess/r 238 ess is therefore 1.28 ± The remainder ratio of 238 U can be estimated in the framework of the open nonlinear GCE model (Dauphas et al., 2003) to be 0.71 for a Galactic age of 13.7 Gyr (0.53 in the closed-box model). The remainder ratio of 244 Pu is thus R 244 ess = 9.1 ± (Dauphas, 2005b). All these ratios are compiled in Table 1. The remainder ratios in the ESS can be compared with those in the ISM as predicted by GCE models. In order to account for the possible isolation of the solar system parent molecular cloud core from fresh nucleosynthetic inputs, a free decay interval ( ) is often introduced (See Clayton, 1983, for a more complicated treatment). This corresponds to a time when radioactive species decay without being replenished by stellar sources. The remainder ratio in the ESS is related to that in the ISM through ( R ess = R ism exp ). (18) τ The remainder ratio in the ISM is itself a function of the mean-life of the considered nuclide (Eq. 14). For radionuclides whose mean-lives are long enough that their abundances in the ESS can be explained by their steady-state abundance in the ISM, combining equations 14 and 18 gives a relationship between the remainder ratios in the ISM and the ESS (Dauphas et al., 2003; Dauphas, 2005b): ( R ess = R ism exp κ TR ism ). (19) The remainder ratios of several short-lived radionuclides determined in the ESS are plotted versus the ISM ratios derived from GCE models in Fig. 4. Also shown are curves corresponding to Eq. 19 calculated with different values of the free decay interval. Some implications of the presence of extinct radionuclides in meteorites on stellar nucleosynthesis and solar system formation are discussed in detail in the following sections.

16 Niobium-92 and the nucleosynthesis of Mo-Ru p-isotopes The radionuclides 53 Mn and 146 Sm define the same free decay interval within uncertainties ( 10 Ma). They were probably synthesized in supernovae and were inherited in the ESS from GCE. Niobium-92 is a special case because it lies in a mass region of the nuclide chart where SN models underproduce p-process isotopes ( 92 Mo, 94 Mo, 96 Ru, and 98 Ru) by a factor of 10 (Rauscher et al., 2002). This nuclide can therefore be used to test the various hypotheses that have been advanced to remedy the underproduction feature of supernovae in the Mo-Ru mass region (Yin et al., 2000; Dauphas et al., 2003) The puzzling origins of extinct r-radioactivities The r-process radionuclides 129 I and 244 Pu were inherited from GCE with a free decay interval of approximately 100 Ma (Fig. 4). If the other r-process nuclides 107 Pd and 182 Hf had been inherited from GCE with the same free decay interval (100 Ma), then their abundances in the ESS would have been much lower than what is observed in meteorites (they require a shorter free decay interval, 30 Ma). The extinct radionuclides 107 Pd and 182 Hf must therefore have a different origin. Two distinct scenarios have been advocated for explaining the origin of these two short-lived nuclides. Wasserburg et al. (1996) and Qian et al. (1998) questioned the universality of the so-called r- process. They suggested that two kinds of r-process events are responsible for the nucleosynthesis of neutron-rich nuclei. One of these events would synthesize heavy r-nuclei and actinides ( 182 Hf and 244 Pu, H-events) while the other would synthesize light r-nuclei ( 129 I, L-events). The H events would occur 10 times more frequently than the L events, which would explain why the free-decay interval inferred from 182 Hf is lower than that inferred from 129 I. Observations of elemental abundances in low-metallicity stars support the view that all r-nuclides are not produced at the same site (Sneden et al., 2000; Hill et al., 2002). Such stars formed early enough in the galactic history that contributions of a limited number of stars can be seen in their spectra. Sneden et al. (2000) analyzed the ultra low-metallicity ([Fe/H]=-3.1) halo star CS and found that low-mass r-process elements such as Y and Ag were deficient compared to expectations based on heavier r-process elements. More recently, Hill et al., (2002) determined the abundance of U, Th, and Eu in another metal poor ([Fe/H]=-2.9) (2002) halo star (CS ). The age of this star based on the U/Th ratio is Gyr (Sect 4.2) which agrees with independent estimates of galactic ages. In contrast, the Th/Eu ratio corresponds to an age that is younger than the age of the Solar System, which is impossible (Hill et al., 2002). This suggests that actinides were produced independently of lighter r-process nuclides. Observations of low-metallicity stars therefore point

17 17 to a multiplicity of r-process events, possibly as many as three. Wasserburg et al. (1996) and Qian et al. (1998) grouped 182 Hf with actinides, including 244 Pu. However, Dauphas (2005b) showed that 244 Pu requires a longer free-decay interval ( 100 Ma) compared to 182 Hf ( 30 Ma). This discrepancy may indicate that, in addition to the L and H events, another event be added to explain actinides (A-events). Note that this would be consistent with observations of lowmetallicity stars which require 3 distinct production sites. According to the multiple r-processes model, 107 Pd was synthesized by the s-process in a low-metallicity, high-mass AGB star that polluted the ESS with a stellar wind (Wasserburg et al., 1994; Gallino et al., 2004). Alternatively, it could have been injected by the explosion of a nearby SN, where it would have been synthesized by the weak s-process (Meyer and Clayton, 2000). Another possible scenario is that the nuclides that are overabundant in the ESS compared to GCE expectations ( 107 Pd and 182 Hf, as well as 26 Al, 36 Cl, 41 Ca, and 60 Fe) were injected in the presolar molecular cloud core by the explosion of a nearby SN that might have triggered the protosolar cloud into collapse (Cameron and Truran, 1977; Meyer and Clayton, 2000; Meyer et al., 2004). The dynamical feasibility of injecting fresh nucleosynthetic products in the ESS has been studied carefully by Vanhala and Boss (2002). In the most recent version of the pollution model, it is assumed that only a fraction of the stellar ejecta is efficiently injected in the nascent solar system (the injection mass cut is the radius in mass coordinates above which the envelope of the SN is injected; Cameron et al., 1995; Meyer et al., 2004). For a 25 M star, an injection mass cut of 5 M, and a time interval of 1 Ma between the SN explosion and incorporation in the ESS, the abundances of 26 Al, 41 Ca, 60 Fe, and 182 Hf are successfully reproduced (Meyer et al., 2004). Chlorine-36 and Palladium-107 are slightly overproduced but this may reflect uncertainties in ESS abundances and input physics. Because the injection scenario requires only one source for explaining all extinct radionuclides that cannot be produced by GCE or irradiation in the ESS while the multiple r-processes scenario requires many, Ockham s razor principle favors the SN pollution model Predicted abundance of 247 Cm in the early solar system Among the short-lived nuclides that have mean lives higher than 5 Ma, only one has eluded detection, 247 Cm (τ = 22.5 Ma, decays to 235 U, Chen and Wasserburg, 1981; Friedrich et al., 2004). Modeling of stellar nucleosynthesis and GCE allows the prediction of its abundance in the ESS. Curium-247 is expected to be produced at the same site that synthesized 129 I and 244 Pu. The same free decay interval can therefore be applied ( = 100±25 Ma). Goriely and Arnould (2001) estimated uncertainties on actinide production ratios. As already discussed in the case of 244 Pu, we only consider the models that give a 238 U/ 232 Th production ratio consistent with the meteoritic

18 18 measurement. The inferred 247 Cm/ 238 U production ratio is ± The remainder ratio in the ISM of 247 Cm can be calculated using the open nonlinear GCE model of Dauphas et al. (2003), R 247 ism = 7.0 ± Using the estimated remainder ratio of 238 U (0.71, see discussion on 244 Pu), we get the ratio of the remainder ratios of 247 Cm and 238 U, R 247 ism /R238 ism = 9.8 ± Allowing for free decay = 100 ± 25 Ma, the ratio in the ESS is R 247 ess/r 238 ess = 1.2 ± This value must be multiplied by the production ratio to get the expected ratio in meteorites. The ratio in the ESS is thus estimated to be 247 Cm/ 238 U = 1.6± ( 247 Cm/ 235 U = 5.0± at solar system formation). The present upper limit for the 247 Cm/ 235 U ratio obtained from U isotopic measurements of meteoritic materials is (Chen and Wasserburg, 1981), which is entirely consistent with the predicted abundance based on modeling of GCE and nucleosynthesis. 5. GCE of stable isotope ratios As discussed above in 2, elemental abundance ratios measured in stars are a powerful tool for constraining models of GCE, because different elements are made by different processes in different types of stars with different evolutionary timescales. This statement is of course not limited to elements, but applies equally well to stable isotope ratios. Many elements are comprised of both primary and secondary isotopes, as defined in 2, so GCE theory anticipates that many isotopic ratios should evolve in the Galaxy. As discussed above, the Simple closed-box GCE model predicts that the ratio of a secondary to a primary isotope increases linearly with metallicity in the Galaxy. As an example, let us consider the stable isotopes of silicon. Numerical supernova nucleosynthetic calculations (Woosley and Weaver, 1995; Timmes and Clayton, 1996) indicate that 28 Si is a primary isotope, whereas 29 Si and 30 Si are secondary. Thus, it is not surprising that the numerical GCE model of Timmes and Clayton (1996) predicts that the 29 Si/ 28 Si and 30 Si/ 28 Si ratios increase monotonically with metallicity. The Si isotopic ratios as a function of metallicity predicted by this model are shown in the left panel of Fig. 5. The secondary nature of the rare Si isotopes is clear. However, it is also immediately apparent that the model does not exactly reproduce the solar isotopic ratios at solar metallicity; the 30 Si/ 28 Si ratio is high by 50% and the 29 Si/ 28 Si ratio is slightly sub-solar. The discrepancy is almost certainly due to errors in the supernova nucleosynthesis calculations that went into the GCE model and agreement within a factor of two is usually considered a success in GCE modeling. However, this is not sufficient for comparison with presolar grain data measured with 1% precision (next section). As discussed at length by Timmes and Clayton (1996), to compare high-precision isotope data with the GCE models in a self-consistent way requires that the models be renormalized so that they reproduce the solar abundances. The simplest approach is to rescale the GCE trends so that they pass through the solar composition at solar metallicity. The renormalized Si isotope trends, scaled in this fashion, are shown in the right panel of Fig. 5. With this renormalization, it is clear that the GCE model predicts that the ratios vary in lockstep